New description of gradual substitution of graft by bone tissue including biomechanical and structural effects, nutrients supply and consumption

Abstract

A new description of graft substitution by bone tissue is proposed in this work. The studied domain is considered as a continuum model consisting of a mixture of the bone tissue and the graft material. Densities of both components evolve in time as a result of cellular activity and biodegradation. The proposed model focuses on the interaction between the bone cell activity, mechanical stimuli, nutrients supply and scaffold microstructure. Different combinations of degradation rate and stiffness of the graft material were examined by numerical simulation. It follows from the calculations that the degradation rate of the scaffold should be tuned to the synthesis/resorption rate of the tissue, which are dependent among the others on scaffold porosity changes. Simulation results imply potential criteria to choose proper bone substitute material in consideration of degradation rate, initial porosity and mechanical characteristics. KeywordsBone regeneration · Bioresorbable and biodegradable material · Microstructure · Nutrients supply · Numerical simulation List of symbols ε Strain σ Stress W s Strain energy ϕ Porosity E Young's modulus d a , d s Normalized sensor/actor cell densities S Mechanical stimulus S 0 Reference stimulus R Nutrients consumption rate z s , z a Sensor/actor cell activities L Coefficient defining the range of stimulus without cell activity A m0 Degradation rate of bone substitute material s b , r b , r m Synthesis / resorption coefficients Communicated by Francesco dell'Isola.

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